Question:
The least value of $x$, for which the expression $x^2 + x + 17$ will not give a prime number, is
The least value of $x$, for which the expression $x^2 + x + 17$ will not give a prime number, is
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Check primality step-by-step until the expression yields a composite number.
Updated On: Aug 11, 2025
- 7
- 11
- 13
- 17
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The Correct Option is D
Solution and Explanation
We substitute values of $x$ into $x^2 + x + 17$ until we find a composite (non-prime) result.
For $x = 7$: $49 + 7 + 17 = 73$ (prime)
For $x = 11$: $121 + 11 + 17 = 149$ (prime)
For $x = 13$: $169 + 13 + 17 = 199$ (prime)
For $x = 17$: $289 + 17 + 17 = 323 = 17 \times 19$ (composite).
Thus, the smallest $x$ for which the expression is not prime is $x = 17$.
For $x = 7$: $49 + 7 + 17 = 73$ (prime)
For $x = 11$: $121 + 11 + 17 = 149$ (prime)
For $x = 13$: $169 + 13 + 17 = 199$ (prime)
For $x = 17$: $289 + 17 + 17 = 323 = 17 \times 19$ (composite).
Thus, the smallest $x$ for which the expression is not prime is $x = 17$.
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